Stability and convergence analysis of hybrid algorithms for Berinde contraction mappings and its applications

Abstract

In this paper, we construct a new hybrid iteration, called SR-iteration, and prove its stability and convergence analysis for weak contraction mappings in a Banach space. We compare the rate of convergence between the SR-iteration and other iterations. Moreover, we provide numerical comparisons for supporting our main theorem and apply our main result to prove the existence problem of mixed type Volterra-Fredholm functional nonlinear integral equation.